I don't think so. I studied Hebrew for 10 years and, once I'd had a couple of years, started taking actual courses in Hebrew. They were taught in modern Hebrew, but the school offered Bible (and rabbinic writing) course, several of which I took. The school (granted, a tiny one) offered no courses in Biblical Hebrew (or rabbinic Hebrew either). The difference between Biblical Hebrew and modern Hebrew is nothing like as great as the difference between Old English, or even Middle English, and present-day English; it's more comparable to the difference between Shakespearean English (known as "modern English" to linguists when I was in school) and present-day English.
I was going to post that I never heard of a translation of the OT into modern Hebrew, but googling reveals that a Baptist publisher in Israel is bringing one out. There's still no Jewish one, though.
One good NT translation is Richmond Lattimore's,
Is that the guy who used to teach ancient Greek as a spoken language at MIT?
Well, not quite as great.
The differences between Israeli Hebrew and Biblical Hebrew are: (1) tons of loanwords from European languages, (2) a pretty much complete abandonment of the Biblical Hebrew tense system and replacement with a modified tense system related to those of European languages and (3) a replacement of Biblical Hebrew's paratactic sentence structure with far more relative clauses and a completely different word order, basically the same sentence structure as English.
The two Hebrews sound much more alike than the two Englishes because most secular Hebrew speakers pronounce Biblical Hebrew and Modern Hebrew in the same way.
The Englishes sound radically different, because the correct ancient pronounciation has been meticulously reconstructed and pronouncing Old English like Modern English is never done.
Is that the guy who used to teach ancient Greek as a spoken language at MIT?
He was not one of the founders of the program, but it would not surprise me if he were one of the visiting professors.